It has recently been proposed that supersymmetric black hole microstates exhibit “fortuity”: their very existence depends sensitively on the finite, precise values of N, the number of degrees of freedom in the dual theory. In this talk, after reviewing the core ideas of fortuity in both large-N gauge theories and toy models such as the SYK model, I will describe a simple matrix...
In large N theories with a gravity dual, generic heavy operators should be dual to black holes in the bulk. The microscopic details of such operators should then be irrelevant in the low energy theory. I will talk about a simple two matrix model -- the Hoppe model -- which also exhibits universality. Using analytics as well as Monte Carlo simulations, I will show that there exists a universal...
I will review recent progress in charting the landscape of two-dimensional (minimal) string theories. This includes novel developments such as the Virasoro minimal string and the complex Liouville string, as well as revisiting the older ADE minimal string models. I will discuss their worldsheet descriptions, their matrix-model duals, and prospects for further directions and generalizations. If...
The IKKT model is a large N matrix integral that arises in string theory as the worldvolume theory of N D-instantons. It holds the promise of being a uniquely tractable model of holographic duality, but has some important differences with other better-understood cases, notably the absence of a time and the related absence of a "decoupling limit” in which the theory is obtained as an isolated...
Recently the Euclidean IKKT model with deformation preserving 16 supersymmetries has attracted a lot of attention. In particular, the partition function was evaluated exactly by applying the SUSY localization method, and the "time-less holography" was discovered. Moreover, it was found that the original IKKT model is NOT retrieved in the limit of removing the deformation. Here we provide a new...
A particularly interesting corner of holographic dualities is the correspondence between type II strings on Dp branes geometries and d = p+1 dimensional super Yang-Mills theories with sixteen supercharges. For the extremal case p=-1, this suggests a holographic duality for the IKKT matrix model. Despite intriguing and highly non-trivial results in the IKKT model, this duality has, until...
I will discuss recent results on matrix models with a focus on the approach to the large N limit. The discussion will include a description of the Hagedorn transition (confining/deconfining transition) and its Hawking-Page dual. It will be argued that in the low temperature regime the canonical and microcanonical descriptions are not equivalent. We will see that negative specific heat can...
The bootstrap method offers a powerful framework for solving theoretical models by systematically solving the optimization problem from the constraints imposed by kinematic and dynamic equalities and inequalities. This approach has demonstrated remarkable efficacy in tackling matrix models, especially in the large N limit and in scenarios complicated by sign problems. In this presentation, we...
The ability to numerically simulates holographic models based on matrix models in their relevant parameter regions is of paramount importance to gain new insights into how the gauge-gravity correspondence is realized away from analytical regimes. New numerical techniques developed for studying quantum many-body physics are being applied to matrix models. I will describe tensor network methods...
I will discuss BPS limits of M-theory that lead to U-dual webs of decoupled theories, whose fundamental degrees of freedom are described by matrix theories. The BPS limits are organized by five different duality orbits of M-theory in DLCQs. Via a generalization of the TTbar deformation to p-branes, this leads to a classification of holographic constructions in string theory. I will show that...
Over 50 years ago, 't Hooft observed the similarity between the Feynman diagram expansion of a large N gauge theory and the topological expansion of a string theory. The purpose of this talk is to make this idea precise for a protected subsector of the AdS/CFT correspondence. Concretely, we show how the Feynman diagram expansion of correlation functions in N=4 SYM preserving half the...
We apply localization to the BFSS matrix model with specific boundary conditions in the time direction, which are related to certain scattering amplitudes in 11-dimensional M-theory. For the boundary conditions corresponding to the three-point graviton amplitude, we compute the partition function exactly using localization and show that the result correctly reproduces the expected momentum...
Interpreting the matrices in the IIB matrix model as representing momentum space, the matrices are described by bilocal fields. Consequently, the IIB matrix model becomes a pregeometric action describing a system that includes gravity. From this perspective, we discuss the possibility that the Standard Model emerges as the effective theory at low energies. This talk is based on joint...
We study matrix theories constructed from non-BPS D-particle/D-instanton systems in type IIA/B string theory. In addition to the matrices describing the positions of the D-particles or D-instantons, these theories contain a tachyonic matrix, which plays a central role. The main claims of this talk are as follows: 1) Any D-brane configuration can, in principle, be realized within these matrix...
I will present a unified D-brane viewpoint on how matrix configurations encode noncommutative and commutative geometries. First, I explain how noncommutative D-branes and fuzzy geometries arise from bound states of infinitely many unstable D0-branes, where tachyon dynamics project to a finite set of effective D0-branes. I will also show that in the same way, we can describe ADHM and Nahm...